B737-800 Captain reported an air data computer failure causing erratic and conflicting readings of airspeed and altitude between the Captain and First Officer's flight instruments. The Captain determined via checklist that the failed instruments were on the Captain side and assigned flying duties to the FO. The FO maintained the flight manual pitch and attitude guidelines; validated airspeed and altitude with ATC; and diverted to a longer runway airport. The flight landed safely at the alternate airport.

Narrative

Experienced airspeed unreliable while descending from FL290 to FL270 on the ZZZZ arrival. My airspeed rolled back quickly. (below 170 knots). Airplane went into control wheel steering. IAS disagree was enunciated. I looked over at the FO's primary flight display and she was near redline. Our altitudes disagreed by nearly 3;000 feet. I knew immediately it was airspeed unreliable. Performed recall and QRC items. I was in a descent in IMC so I set the N1 to 80% and pitch to 4 degrees. Asked ATC for a block altitude. Also verified my altitude and ground speed with ATC continuously. After performing QRC and QRH it was determined that my side was the erroneous side. Assigned flying duties to the FO. I [requested priority handling] and chose ZZZ1 as a diversion destination instead of ZZZ2. Completed non routine landing considerations and safely landed in ZZZ1. On a side note: I would like to take this opportunity to commend our training department. I have practiced this exact scenario in the sim and it played out in real life virtually the same. Because it was practiced in the sim my startle factor was not nearly as high. Cause - Mechanical malfunction.Suggestions - Nothing could have prevented this. After speaking with maintenance it was determined that the #1 ADIRU failed.